Solve {(e)^frac{-199*10^-19{138*10^-23*300}}}

$${(e)^{ \frac{ -199 \times { 10 }^{ -19 } }{ 138 \times { 10 }^{ -23 } \times 300 } }}$$

Evaluate

$$\frac{1}{e^{\frac{9950}{207}}}\approx 1.331963411 \cdot 10^{-21}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$e^{\frac{-199\times 10^{4}}{138\times 300}}$$

Calculate 10 to the power of 4 and get 10000.

$$e^{\frac{-199\times 10000}{138\times 300}}$$

Multiply -199 and 10000 to get -1990000.

$$e^{\frac{-1990000}{138\times 300}}$$

Multiply 138 and 300 to get 41400.

$$e^{\frac{-1990000}{41400}}$$

Reduce the fraction \frac{-1990000}{41400} to lowest terms by extracting and canceling out 200.

$$e^{-\frac{9950}{207}}$$